Abstract

We propose and theoretically demonstrate an all-optical method for directly generating all-optical random numbers from pulse amplitude chaos produced by a mode-locked fiber ring laser. Under an appropriate pump intensity, the mode-locked laser can experience a quasi-periodic route to chaos. Such a chaos consists of a stream of pulses with a fixed repetition frequency but random intensities. In this method, we do not require sampling procedure and external triggered clocks but directly quantize the chaotic pulses stream into random number sequence via an all-optical flip-flop. Moreover, our simulation results show that the pulse amplitude chaos has no periodicity and possesses a highly symmetric distribution of amplitude. Thus, in theory, the obtained random number sequence without post-processing has a high-quality randomness verified by industry-standard statistical tests.

K. Huybrechts, A. Ali, T. Tanemura, Y. Nakano, and G. Morthier, “Numerical and experimental study of the switching times and energies of DFB-laser based All-optical flip-flops,” presented at the International Conference on Photonics in Switching, Pisa, Italy, 15–19 Sept. 2009.

Other (4)

K. Huybrechts, A. Ali, T. Tanemura, Y. Nakano, and G. Morthier, “Numerical and experimental study of the switching times and energies of DFB-laser based All-optical flip-flops,” presented at the International Conference on Photonics in Switching, Pisa, Italy, 15–19 Sept. 2009.

Random bit patterns with 300 × 300 bits are shown in a two-dimensional plane. Bits “1” and “0” are converted to white and black dots, respectively, and placed from left to right (and from top to bottom).

The frequency of “0” in a random bit sequence (black squares) and the number of passed NIST tests (blue circles) as a function of the threshold bias. Here the threshold bias represents the difference between the threshold of the all-optical flip-flop (AOFF) which is fixed at 0.1 mW and the average power of the chaotic pulse trains.

Tables (2)

Table 1 Typical results of NIST statistical tests. Using 1000 samples of 1 Mb data and significance level α = 0.01, for “Success”, the P-value (uniformity of p-values) should be larger than 0.0001 and the proportion should be greater than 0.9805608.

Table 2 Typical results of Diehard statistical tests. Using 74 Mb data and significance level α = 0.01, for “Success”, the P-value (uniformity of p-values) should be larger than 0.0001. “KS” indicates that single P-value is obtained by the Kolmogorov-Smirnov (KS) test.

Metrics

Table 1

Typical results of NIST statistical tests. Using 1000 samples of 1 Mb data and significance level α = 0.01, for “Success”, the P-value (uniformity of p-values) should be larger than 0.0001 and the proportion should be greater than 0.9805608.

STATISTICAL TEST

P-value

Proportion

Result

Frequency

0.864510

0.9950

Success

Block frequency

0.104102

0.9860

Success

Cumulative sums

0.452681

0.9940

Success

Runs

0.119896

0.9830

Success

Longest-run

0.308143

0.9940

Success

Rank

0.699774

0.9950

Success

FFT

0.801956

0.9860

Success

Non-periodic templates

0.030957

0.9930

Success

Overlapping templates

0.444908

0.9890

Success

Universal

0.339508

0.9870

Success

Approximate entropy

0.630192

0.9950

Success

Random excursions

0.125470

0.9830

Success

Random excursions variant

0.198021

0.9900

Success

Serial

0.736782

0.9920

Success

Linear Complexity

0.561793

0.9910

Success

Table 2

Typical results of Diehard statistical tests. Using 74 Mb data and significance level α = 0.01, for “Success”, the P-value (uniformity of p-values) should be larger than 0.0001. “KS” indicates that single P-value is obtained by the Kolmogorov-Smirnov (KS) test.

STATISTICAL TEST

P-value

Result

Birthday spacing

0.546187

Success

KS

Overlapping 5-permutation

0.447600

Success

Binary rank for 31 × 31 matrices

0.564080

Success

Binary rank for 32 × 32 matrices

0.627815

Success

Binary rank for 6 × 8 matrices

0.876204

Success

KS

Bitstream

0.145736

Success

Overlapping-Pairs-Space-Occupancy

0.087900

Success

Overlapping-Quadruples-Space-Occupancy

0.105129

Success

DNA

0.383215

Success

Count –the-1’s on a stream of bytes

0.152096

Success

Count –the-1’s for specific bytes

0.120932

Success

Parking lot

0.644797

Success

KS

Minimum distance

0.958178

Success

KS

3D-spheres

0.743550

Success

KS

Squeeze

0.623810

Success

Overlapping sums

0.631732

Success

KS

Runs

0.423050

Success

KS

Craps

0.552007

Success

Tables (2)

Table 1

Typical results of NIST statistical tests. Using 1000 samples of 1 Mb data and significance level α = 0.01, for “Success”, the P-value (uniformity of p-values) should be larger than 0.0001 and the proportion should be greater than 0.9805608.

STATISTICAL TEST

P-value

Proportion

Result

Frequency

0.864510

0.9950

Success

Block frequency

0.104102

0.9860

Success

Cumulative sums

0.452681

0.9940

Success

Runs

0.119896

0.9830

Success

Longest-run

0.308143

0.9940

Success

Rank

0.699774

0.9950

Success

FFT

0.801956

0.9860

Success

Non-periodic templates

0.030957

0.9930

Success

Overlapping templates

0.444908

0.9890

Success

Universal

0.339508

0.9870

Success

Approximate entropy

0.630192

0.9950

Success

Random excursions

0.125470

0.9830

Success

Random excursions variant

0.198021

0.9900

Success

Serial

0.736782

0.9920

Success

Linear Complexity

0.561793

0.9910

Success

Table 2

Typical results of Diehard statistical tests. Using 74 Mb data and significance level α = 0.01, for “Success”, the P-value (uniformity of p-values) should be larger than 0.0001. “KS” indicates that single P-value is obtained by the Kolmogorov-Smirnov (KS) test.